Wang, Weiren and Zhou, Mai
(1995):
*Iterative Least Squares Estimator of Binary Choice Models: a Semi-Parametric Approach.*

Preview |
PDF
MPRA_paper_46981.pdf Download (1MB) | Preview |

## Abstract

Most existing semi-parametric estimation procedures for binary choice models are based on the maximum score, maximum likelihood, or nonlinear least squares principles. These methods have two problems. They are difficult to compute and they may result in multiple local optima because they require optimizing nonlinear objective functions which may not be unimode. These problems are exacerbated when the number of explanatory variables increases or the sample size is large (Manski, 1975, 1985; Manski and Thompson, 1986; Cosslett, 1983; Ichimura, 1993; Horowitz, 1992; and Klein and Spady, 1993).

In this paper, we propose an easy-to-compute semi-parametric estimator for binary choice models. The proposed method takes a completely different approach from the existing methods. The method is based on a semi-parametric interpretation of the Expectation and Maximization (EM) principle (Dempster et al, 1977) and the least squares approach. By using the least squares method, the proposed method computes quickly and is immune to the problem of multiple local maxima. Furthermore, the computing time is not dramatically affected by the number of explanatory variables. The method compares favorably with other existing semiparametric methods in our Monte Carlo studies. The simulation results indicate that the proposed estimator is, 1) easy-to-compute and fast, 2) insensitive to initial estimates, 3) appears to be root(n)-consistent and asymptotically normal, and, 4) better than other semi-parametric estimators in terms of finite sample performances. The distinct advantages of the proposed method offer good potential for practical applications of semi-parametric estimation of binary choice models.

Item Type: | MPRA Paper |
---|---|

Original Title: | Iterative Least Squares Estimator of Binary Choice Models: a Semi-Parametric Approach |

English Title: | Iterative Least Squares Estimator of Binary Choice Models: a Semi-Parametric Approach |

Language: | English |

Keywords: | Binary choice models, EM algorithm, least squares method, semi-parametric estimation. |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities |

Item ID: | 46981 |

Depositing User: | Weiren Wang |

Date Deposited: | 16 May 2013 06:31 |

Last Modified: | 28 Sep 2019 15:03 |

References: | [1] AMEMIYA, T.: Advanced Econometrics, Cambridge, Mass: Harvard University Press, 1985. [2] AYER, M. H. D. BRUNK, G. M. Ev ING, W. T. REID, AND E. SILVERMAN (1955): "An Empirical Distribution Function for Sampling with Incomplete Information,," Annals of Mathematical Statistics, 26, 641-647. [3] BUCKLEY, J. AND I. JAMES (1979):"Linear Regression with Censored Data," Biometrika, 66, 429-436. [4] COSSLETT, S. R. (1983):"Distribution-free Maximum Likelihood Estimator of the Binary Choice Model," Econometrica 51, 765-782. [5] COSSLETT, S. R. (1986): "Efficiency of Semiparametric Estimators for the Binary Choice Model in Large Samples: A Monte Carlo Comparison," manuscript. [6] COSSLETT, S. R. (1987): "Efficiency Bounds for Distribution-Free Estimators of the Binary Choice and the Censored Regression Models," Econometrica, 55, 559-585. [7] DEMPSTER, A. P. N. M. LAIRD, AND D. R. RUBIN (1977): "Maximum Likelihood Estimation from Incomplete Data via the EM Algorithm," (with Discussion) Journal of the Royal Statistical Society, Series B, 39, 1-38. [8] EFRON, B. (1982):"The Jackknife, the Bootstrap and Other Resampling Plans," CBMSNSF Regional Conference Series in Applied Mathematics, 38. [9] GABLER, S. LAISNEY, F. AND M. LECHNER (1993):"Seminonparametric Estimation of Binary-Choice Models with an Application to Labor-Force Participation," Journal of Business & Economic Statistics, 11, 61-80. [10] GREENE, W. H. : Econometric Analysis, New York: MacMillan Publishing Company, Second Edition, 1993. [11] GROENEBOON, P. AND J. A. WELLNER: Information Bounds and Nonparametric Maximum Likelihood Estimation, Basel: BirkhĂ¤user, 1992. [12] HAN, A. K. (1987):"Non-Parametric Analysis of a Generalized Regression Model," Journal of Econometrics, 35, 303-316. [13] Horowitz, J. L. (1992):"A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, 60, 505-531. [14] Horowitz, J. L. (1994): "Advances in Random Utility Models," Working Paper Series No.94-02, Department of Economics, University of Iowa. [15] HUBER, P. J. (1967):"The behavior of Maximum Likelihood Estimates Under Nonstandard Conditions," Proceedings of the Fifth Berkeley Symposium in Mathematical Statistical and Probability. Berkeley: University of California. [16] ICHIMURA, H. (1993):"Semiparametric Least Square (SLS) and Weighted SLS Estimation of Single-Index Models," Journal of Econometrics, 58, 71-120. [17] ICHIMURA, H. AND T. S. THOMPSON (1993):"Maximum Likelihood Estimation of a Binary Choice Model with Random Coefficients of Unknown Distribution," memo, September 1993. [18] KIM, J., AND D. POLLARD (1990):"Cube Root symptotics," Annals of Statistics 18, 191-219. [19] KLEIN, R. L. AND R. H. SPADY (1993):"An Efficient Semiparametric Estimator for Discrete Choice Models," Econometrica, 61, 387-421. [20] LEURGANS, S. (1982): "Asymptotic distributions of slope-of-greatest-convex-minorant estimators," Annals of Statistics, 10, 287-296. [21] MADDALA, G. S.: Limited Dependent and Qualitative Variables in Econometrics, New York: Cambridge University Press, 1983. [22] MANSKI, C. (1975):"Maximum Score Estimation of the Stochastic Utility Model of Choice," Journal of Econometrics, 3, 205-228. [23] MANSKI, C. (1985):"Semiparametric Analysis of Discrete Response: Asymptotic Properties of the Maximum Score Estimator," Journal of Econometrics, 27, 313-334. [24] MANSKI, C. AND T. S. THOMPSON (1986):"Operational Characteristics of Maximum Score Estimation," Journal of Econometrics, 32, 65-108. [25] MATZKIN, R. L. (1992):"Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models," Econometrica, 60, 239-270. [26] PINKSE, C. A. P. (1993):"On the Computation of Semiparametric Estimates in Limited Dependent Variable Models," Journal of Econometrics, 58, 185-205. [27] POLLARD, D.: Convergence of Stochastic Processes , New York: Springer-Verlag, 1984. [28] RUUD, P. A. (1983):"Sufficient Conditions for the Consistency of Maximum Likelihood Estimation despite Misspecification of Distribution," Econometrica, 49, 505-514. [29] SHERMAN, R. P. (1993):"The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, 61, 123-138. [30] VAN DER VAART, A. W. (1991):"On Differentiable Functionals," Annals of Statistics, 19, 178-205. [31] Wu, C. F. J. (1986):"Jackknife, Bootstrap and Other Resampling methods in Regression Analysis," Annals of Statistics, 14, 1261-1295. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/46981 |